Google would be your friend on this. A good start would be to simply search "Dean Radin". He has done research of his own, but is also pretty much the current standardbearer in this area, and you will find abundant links connected to his name. If you nose around a bit, you can also find the entire history of the ganzfeld research and all of the back-and-forth that has gone with it. Odds against chance in much of this research are huge, and that is sometimes used as a point against it: that such odds cannot be attained in any normal experimental circumstance, and therefore must be spurious in this case, especially. But the research is carefully done, statistical techniques have indeed sprung into being in pursuit of more rigorous ways to test these results, and although the mainstream scientific community has certainly not accepted them by any means, I personally find the results difficult to dismiss as chance. Everybody has an ontology, and no one likes results that seem to overturn it. Results such as these certainly upset the apple cart.
Other research that extends back many decades originates in the work of the Frenchman Rene Warcollier and concerns clairvoyance, specifically the kinds of drawings that are now done under the name of "remote viewing". Remote viewing is simply clairvoyance couched in military parlance, and the field is absolutely rife with ex-Army nutcases spending their time on shows like Coast-To-Coast talking about alien invasions and whatnot. But the core of this research is interesting in that a) demonstrable results have been achieved on a repeated basis and b) the phenomena are lawful in the sense that drawings made by "viewers" not in normal contact with the target deviate from those targets in predictable ways. Objects may be broken down into details: squares become represented by a set of right angles, the American flag is broken down into a set of parallel lines, a rectangle, and an elongated cylinder, all rendered separately, and the viewer has no idea of the relation between them. And it's interesting that there are parallels between these phenomena and those found in patients with brain lesions, in this case lesions of the right hemisphere.
To summarize, the research is if you look for it, and resist the urge to make a 'skeptic' site your first (and only) stop. Even searching a term such as "remote viewing"—which will dredge up a lot of crazies—will provide evidence that something is going on here. Add to that the ganzfeld research and earlier efforts extending back decades, and it becomes clear that it's unwarranted to dismiss the field out-of-hand. Some of the best stuff really comes from Warcollier—there's nothing statistically satisfying here, because he didn't do statistics, but the lawfulness of the phenomena are well demonstrated in the couple of books out by him. Ultimately, it's more satisfying. But unfortunately, there's a real paucity of work by the man available on the internet. The refrain "there is no evidence" simply isn't true. It's just something repeated over and over, and I think often by people who have an evangelical conviction against these phenomena from the get-go. You do have to look in the right places—nothing will change the reality that literally 95% of what you find in this topic area is utter bollocks written by New Age flakes. But research results are out there, and they're not easily set aside, in spite of what some would have you believe.
"Here's something to think about: How come you never see a headline like `Psychic Wins Lottery.'" -- Comedian Jay Leno